It is well known that in the billiard and snooker games there are cues of different lengths and consequently slightly different diameters at the butt end, more particularly from 30 to 33 mm. It is also necessary to have at disposal at least one standard cue and one longer cue for particular shots, when the ball to be hit is in a position that cannot be reached with the standard cue. Indeed, players of a certain level generally have their own personal cue and do not like to make recourse to the longer cues available in the billiard halls and use an extension to be applied on their personal cue. However the means presently available for inserting the extension are not very satisfactory and more particularly cannot be used for cues of any diameter. The object of the present invention is therefore to provide a universal joint for extensions of billiard cues allowing to insert an extension on the standard cues, of any diameter at the butt end.